You can get even closer than using hexagons or squares by joining pointed oval shapes together ("gores"), with pattens like those used for making globe-type maps from paper or cardstock.
FORGET what I said below... just check out these links:
http://www.purlbee.com/fabric-beach-balls
http://www.google.com/search?q=how+to+make+fabric+ball+round
If you're interested in those, check out some of these links:
http://www.gma.org/surfing/imaging/globe.html
http://myweb.tiscali.co.uk/greavesandthomas/paper_globes.html
http://www.korthalsaltes.com/globe.html
http://netpbm.sourceforge.net/doc/ppmglobe.html
This would be kind of hard with fabric since you'd have to add seam allowances too, or perhaps you could make the ball inside out and put some kind of adhesive strip over each join in the gores rather than using seam allowances. Do all but the final join, turn inside out, then carefully glue or butt and sew the final seam?
Here's another type and pattern:
http://en.wikipedia.org/wiki/Dymaxion_map
HTH,
Diane B.